How to create an arch (vault) that is curved inside?
A Gothic vault is usually the intersection of Gothic arch prisms. For the basic shape:

Starting with a quarter of a circle, Z up, X accross, snap set to Vertex' and'Active'


Duplicate the vertex on X=0, drop it in Z, to give something to snap to
Under a mirror modifier in X with 'Merge' and 'Clip' checked, select all the vertices on the arc with the desired peak vertex active, and GX snap the half-arches together.





Discard excess vertices, and E extrude in Y





Create an empty at the origin, in this case, rotated in Z by 45 degrees
Assign an Array modifier ('Merge' and 'First and Last' checked) to the extrusion, Object Offset, with the empty as target.
Here, I used the shipped 'TinyCad' add-on to create the vertices shown active, at the intersection of perimeter edges.
K with Z cut through, from the new vertex to the center.





Select the external faces to be retained, CtrlI invert the selection, and X delete unwanted faces.
Here, I've also K with C to constrain to horizontal in a top view, cut the circumferential edges
If you want to bevel the peaks and troughs, select the edge-loops before applying the modifiers to a copy of the object, and bevel after applying.




The result.



Obviously there may be other actions you want to take while under the modifiers, to tweak / decorate / create suitable topology for columns, etc.